Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 32 [2] (1998)Páginas 143-172

Sobre el comportamiento asintótico de algunas sucesiones de polinomios generadas por fórmulas lineales de recurrencia de segundo orden

Yu Takeuchi
Universidad Nacional de Colombia, Bogotá

Abstract. The asymptotic behavior of systems of polynomials defined by linear second order recurrence relations of the form; where , is studied. As an application of the results, the domains of convergence of polynomial series of the form 1 with lim sup are determined, and the well known Abel's lemma for power series is extended to such series under appropriate assumptions. The latter problem had been previously addressed by professor Miguel Dumett in [3] from a different point of view.

Palabras claves. Linear second order recurrence relations, independen solutions, asymptotic behavior of solutions, bounded and uniformly bounded variation, Chebyshev, Legendre, Gegenbauer and Jacobi polynomials, Abel-Picard convergence.

Codigo AMS. 1991 Primary 42C05. Secondary 42C10, 42C15.

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